Synchronize an object following a path and the appearance of the path
In the example file where the curve object has keyframes set to animate the curve geometry end, change the Bevel Factor type to Spline and set the interpolation of the keyframes to linear.


The different Bevel Factor modes for start and end are:
RESOLUTION:
Resolution Map the bevel factor to the number of subdivisions of a spline (U resolution).
SEGMENTS
Segments, Map the bevel factor to the length of a segment and to the number of subdivisions of a segment.
SPLINE
Spline, Map the bevel factor to the length of a spline.